Relevance of the type III error in epidemiological maps

Heinzl Harald, Waldhoer, Waldhoer Thomas

Description

A type III error arises from a two-sided test, when one side is erroneously favoured although the true effect actually resides on the other side. The relevance of this grave error in decision-making is studied for epidemiological maps. Results Theoretical considerations confirm that a type III error may be large for regions with small numbers of expected cases even when no spatial smoothing has been performed. A simulation study based on infant mortality data in Austria reveals that spatial smoothing may additionally increase the risk of type III errors. Conclusions The occurrence of a type III error should be taken into account when interpreting results presented in epidemiological maps, particularly with regard to sparsely populated regions and spatial smoothing.

Sujets

• Statistical power
• Infant mortality

Informations

• Publié par: biomed
• Publié le: 01 janvier 2012
• Nombre de lectures: 5
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Heinzl and WaldhoerInternational Journal of Health Geographics2012,11:34 http://www.ijhealthgeographics.com/content/11/1/34

INTERNATIONAL JOURNAL OF HEALTH GEOGRAPHICS

R E S E A R C HOpen Access Relevance of the type III error in epidemiological maps 1 2* Harald Heinzland Thomas Waldhoer

Abstract Background:type III error arises from a twosided test, when one side is erroneously favoured although the trueA effect actually resides on the other side. The relevance of this grave error in decisionmaking is studied for epidemiological maps. Results:Theoretical considerations confirm that a type III error may be large for regions with small numbers of expected cases even when no spatial smoothing has been performed. A simulation study based on infant mortality data in Austria reveals that spatial smoothing may additionally increase the risk of type III errors. Conclusions:The occurrence of a type III error should be taken into account when interpreting results presented in epidemiological maps, particularly with regard to sparsely populated regions and spatial smoothing. Keywords:Directional test decision, Statistical power, Infant mortality, Standardised mortality ratio (SMR), Crude SMR estimator, Unstructured random effect, Structured random effect, BYM model

Background Epidemiological maps, also known as spatial maps or choropleth maps, are widely used, especially since the ad vent of powerful and userfriendly geographic information system (GIS) software tools. Among other aspects, public health indicators and health care performance measures are shown in graphic form on the basis of these maps. By way of an example, Figure 1 shows standardised mortality ratios (SMRs) of infant mortality across 121 Austrian districts. SMR is a common epidemiological indicator for present ing and studying mortality in a spatial context. Three approaches to estimate the SMR will be considered in the following: crude, unstructured, and BesagYorkMollié (BYM) [1]. ThecrudeSMR is obtained by simply dividing the num ber of observed cases of a spatial unit by its corresponding number of expected cases. For the purpose of generalisabil ity, it would be meaningful to consider crude SMR as being based on a simple Poisson model. Thus, theunstructured SMR may be considered to be based on a Poisson model, including a spatially unstructured random effect. BYM SMR is based on a Poisson model, including a spatially

* Correspondence: [e-mail] 2 Department of Epidemiology, Center for Public Health, Medical University of Vienna, Borschkegasse 8a, A1090, Vienna, Austria Full list of author information is available at the end of the article

unstructured and a spatially structured random effect [1]. However, a Poisson model with a spatially structured ran dom effect alone (i.e. a structured SMR approach), such as the conditionally autoregressive (CAR) model, is not con sidered in the present report. In the simplest form the expected cases are derived by multiplying the overall nationwide mortality rate with the number of population years of the spatial unit of interest. More refined approaches utilise the available covariate information as well. The variability of the crude SMR estimator strongly depends on the size of the population of the respective spatial unit. This may yield extreme estimates, especially for sparsely populated spatial units. Nowadays the crude SMR is rarely used in spatial epidemiology. However, as it is the origin of all types of SMR estimators, it will be studied here for the purpose of comparison. The incorporation of spatially unstructured and/or spatially structured random effects into SMR estimation is also known as spatial smoothing. The concept under lying spatial smoothing is "borrowing strength" from neighbouring spatial units in order to avoid extreme SMR estimates by flattening out random noise fluctua tions. In practice, the computational implementation of spatial smoothing is usually performed in the context of a Bayesian statistical approach.

© 2012 Heinzl and Waldhoer; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.